Overlap as function of distance

In summary, the conversation discusses how to calculate the overlap integral between atomic orbitals on two different atoms, and how this becomes more complicated when considering two molecules. The use of spherical polar coordinates and equations for spherical harmonics and radial wavefunctions is mentioned. The potential distortion of orbitals due to the presence of other atoms is also noted. The idea of using Slater wave functions and inner products of chosen wave functions to measure overlap is brought up, with the question of whether only the parts of the wave functions that see each other should be considered.
  • #1
ftft
21
0
I am trying to find a way to calculate the overlap integral between atomic orbitals centred on two different atoms, A & B as a function of the separation distance. I hope someone in the forum can give a hint on how to do that.
Thanks,
ftft
 
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  • #2
Since orbitals are normally written in spherical polar coordinates, you'll have to convert them into Cartesian coordinates. I assume you know the equations for the spherical harmonics and the radial wavefunction. But the orbitals also get distorted by the presence of the other atom, so it becomes hard.
 
  • #3
That's a good point Khashishi..
OK.. what if we generalize the problem to two molecules, A & B? each will then have molecular orbitals made by LCAO. To measure overlap in this case: Do we use the Slater wave function (which is determinant of LCAOs including occupied and empty orbitals) for each molecule? Or is it enough to compose the wave function from occupied orbitals? Mathematically, is it enough to calculate the inner product of the two (chosen) wave functions? I am assuming that only those parts of the two wave functions which see each other will contribute to the overlap integral.. how mathematically can we restrict the overlap a small part of the wave functions?
 

1. What does "overlap as function of distance" mean?

Overlap as function of distance refers to the relationship between the distance between two objects and the amount of overlap or shared space between them. It is a measure of how much two objects occupy the same space, and how this relationship changes as the distance between them changes.

2. Why is overlap as function of distance important in science?

Overlap as function of distance is important because it helps us understand interactions between objects and how they affect each other. It is particularly relevant in fields such as physics, chemistry, and biology, where understanding the spatial relationships between objects is crucial to understanding their behavior and properties.

3. How is overlap as function of distance measured?

Overlap as function of distance can be measured using various techniques, depending on the specific objects and their properties. Some common methods include microscopy, spectroscopy, and mathematical modeling. These methods allow us to visualize and quantify the amount of overlap between objects at different distances.

4. What factors affect the overlap as function of distance?

Several factors can influence the overlap as function of distance between two objects. These include the size, shape, and properties of the objects, as well as the type of interaction between them. Other external factors, such as temperature and pressure, can also affect the amount of overlap between objects.

5. How can we apply overlap as function of distance in real-world situations?

Overlap as function of distance has many practical applications in various fields. For example, it can help us understand the stability and reactivity of molecules in chemistry, the behavior of particles in physics, and the interactions between cells in biology. It can also be used to develop new materials, optimize industrial processes, and improve our understanding of natural phenomena.

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